Morse matchings on polytopes

We show how to construct homology bases for certain CW complexes in terms of discrete Morse theory and cellular homology. We apply this technique to study certain subcomplexes of the half cube polytope studied in previous works. This involves constructing explicit complete acyclic Morse matchings on the face lattice of the half cube; this procedure may be of independent interest for other highly symmetric polytopes

Mechanics and force transmission in soft composites of rods in elastic gels

We report detailed theoretical investigations of the micro-mechanics and bulk elastic properties of composites consisting of randomly distributed stiff fibers embedded in an elastic matrix in two and three dimensions. Recent experiments published in Physical Review Letters [102, 188303 (2009)] have suggested that the inclusion of stiff microtubules in a softer, nearly incompressible biopolymer matrix can lead to emergent compressibility. This can be understood in terms of the enhancement of the compressibility of the composite relative to its shear compliance as a result of the addition of stiff rod-like inclusions. We show that the Poisson's ratio $\nu$ of such a composite evolves with increasing rod density towards a particular value, or {\em fixed point}, independent of the material properties of the matrix, so long as it has a finite initial compressibility. This fixed point is $\nu=1/4$ in three dimensions and $\nu=1/3$ in two dimensions. Our results suggest an important role for stiff filaments such as microtubules and stress fibers in cell mechanics. At the same time, our work has a wider elasticity context, with potential applications to composite elastic media with a wide separation of scales in stiffness of its constituents such as carbon nanotube-polymer composites, which have been shown to have highly tunable mechanics.Comment: 10 pages, 8 figure

Bacteremic Pneumococcal Pneumonia: a Longitudinal Study in 279 Adult Patients from a Single Center

Background: Bacteremic pneumococcal pneumonia (BPP) is the most common clinical presentation of invasive pneumococcal disease (IPD). Although it has been extensively studied, there is little knowledge in our region in relation to burden of disease, demographic and outcome features. Methods: We conducted a prospective, longitudinal, observational study from 1989 to 2015 in adult patients with BPP, in order to deepen our knowledge of the characteristics of this disease in our community hospital in Tandil, Argentina. Results: 279 patients were included. The mean incidence was 2.8/1000 admissions with a sharp decrease in the last two years, reaching 0.8/1000 admissions. Mean patient age was 60 years. Comorbidities were found in 65% of the cases. Non-respiratory symptoms occurred in 50% of cases. Infiltrates on chest x ray were predominantly unilateral (75%) and lobar (57%). Regarding severity, a low PSI score I-II-II was found in 178 patients (64%), 60 (22%) were admitted to ICU, 40 (14%) required mechanical ventilation, and 21 (8%) developed empyema. Penicillin resistance was not found. Mortality was 18% (49/279), and by a multivariate analysis it was associated with confusion (OR= 5.44), age\u3e80 years (OR =5.72), leukopenia (OR =5.73) and dyspnea (OR=7.87). Conclusions: In this study of 279 bacteremic pneumococcal pneumonia we reinforce previous knowledge on this disease regarding incidence and clinical features and confirm a considerable an early mortality associated to age and severity of disease at onset. Recent changes in incidence of BPP in adults could be secondary to herd effect of PVC 13 a vaccine that is mandatory in children in our community since 2012

A second look at the toric h-polynomial of a cubical complex

We provide an explicit formula for the toric $h$-contribution of each cubical shelling component, and a new combinatorial model to prove Clara Chan's result on the non-negativity of these contributions. Our model allows for a variant of the Gessel-Shapiro result on the $g$-polynomial of the cubical lattice, this variant may be shown by simple inclusion-exclusion. We establish an isomorphism between our model and Chan's model and provide a reinterpretation in terms of noncrossing partitions. By discovering another variant of the Gessel-Shapiro result in the work of Denise and Simion, we find evidence that the toric $h$-polynomials of cubes are related to the Morgan-Voyce polynomials via Viennot's combinatorial theory of orthogonal polynomials.Comment: Minor correction